Related papers: Homology of SL2 over function fields I: parabolic …

In this paper we classify curves of genus two over a perfect field k of characteristic two. We find rational models of curves with a given arithmetic structure for the ramification divisor and we give necessary and sufficient conditions for…

The factorization number $F_2(G)$ of a finite group $G$ is the number of all possible factorizations of $G=HK$ as product of its subgroups $H$ and $K$, while the subgroup commutativity degree $\mathrm{sd}(G)$ of $G$ is the probability of…

In his previous papers the author proved that in characteristic different from 2 the jacobian J(C) of a hyperelliptic curve C: y^2=f(x) has only trivial endomorphisms over an algebraic closure K_a of the ground field K if the Galois group…

For D an infinite set, k>1 and W the set of k-sets from D, there is a natural closed permutation group G_k which is a non-split extension of \mathbb{Z}_2^W by \Sym(D). We classify the closed subgroups of G_k which project onto \Sym(D)$. The…

We characterize homology manifolds with $g_2\leq 2$. Specifically, using retriangulations of simplicial complexes, we give a short proof of Nevo and Novinsky's result on the characterization of homology $(d-1)$-spheres with $g_2=1$ for…

We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem explores the construction of nerves for Lie 2-categories,…

Let $F$ be a p-adic local field and $G=GL_2(F)$. Let $\mathcal{H}^{(1)}$ be the pro-p Iwahori-Hecke algebra of $G$ with coefficients in an algebraic closure of $\mathbb{F}_p$. We show that the supersingular irreducible…

Let $G$ be a connected reductive group over a perfect field $k$. We study a certain normal reductive monoid $\overline M$ associated to a parabolic $k$-subgroup $P$ of $G$. The group of units of $\overline M$ is the Levi factor $M$ of $P$.…

We construct families of hyperelliptic curves over Q of arbitrary genus g with (at least) g integral elements in K_2. We also verify the Beilinson conjectures about K_2 numerically for several curves with g=2, 3, 4 and 5. The paper is…

We study bundle gerbes on manifolds $M$ that carry an action of a connected Lie group $G$. We show that these data give rise to a smooth 2-group extension of $G$ by the smooth 2-group of hermitean line bundles on $M$. This 2-group extension…

Let $H=H_q(n)$ be the Hecke algebra of the symmetric group of degree n, over a field of arbitrary characteristic, and where q is a primitive l-th root of unity in $K$. Let $H_{\rho}$ be an l-parabolic subalgebra of $H$. We give an…

We introduce the adjoint homological Selmer module for an SL$_2$-representation of a knot group, which may be seen as a knot theoretic analogue of the dual adjoint Selmer module for a Galois representation. We then show finitely generated…

We characterize the biharmonic curves in the special linear group $SL(2,R)$. In particular, we show that all proper biharmonic curves in $SL(2,R)$are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean…

Let $A$ be a commutative algebra over the field ${\mathbb F}_2 = {\mathbb Z}/2$. We show that there is a natural algebra homomorphism $\ell (A) \to HC^-_*(A)$ which is an isomorphism when $A$ is a smooth algebra. Thus, the functor $\ell$…

This paper investigates the structure of $K_2$-groups for certain quotient rings of the integral group ring $\mathbb{Z}[G]$. Let $G$ be a finite abelian $p$-group with $p$-rank $r$, let $\Gamma$ be the maximal $\mathbb{Z}$-order of…

Starting from a 6-dimensional nilpotent Lie group N endowed with an invariant SU(3) structure, we construct a homogeneous conformally parallel G_2-metric on an associated solvmanifold. We classify all half-flat SU(3) structures that endow…

Given a smooth non-hyperelliptic curve C of genus 3 and a maximal isotropic subgroup (w.r.t. the Weil pairing) L in Jac(C)[2], there exists a smooth curve C' s.t. Jac(C')=Jac(C)/L. This construction is symmetric. i.e. if we start with C'…

Let G be a group acting on a tree with cyclic edge and vertex stabilizers. Then stable commutator length (scl) is rational in G. Furthermore, scl varies predictably and converges to rational limits in so-called "surgery" families. This is a…

We establish an analog of a theorem of Stallings which asserts the homomorphisms between the universal nilpotent quotients induced by a homomorphism $G \to H$ of groups are isomorphisms provided a pair of homological conditions are…

For a field $k$, we prove that the $i$th homology of the groups $GL_n(k)$, $SL_n(k)$, $Sp_{2n}(k)$, $SO_{n,n}(k)$, and $SO_{n,n+1}(k)$ with coefficients in their Steinberg representations vanish for $n \geq 2i+2$.